Download -Through Capability of a Single-Stage Single-Phase Photovoltaic Low Voltage Ride -Voltage Grid

Low Voltage Ride-Through Capability of a Single-Stage Single-Phase Photovoltaic
System Connected to the Low-Voltage Grid
Yongheng Yang and Frede Blaabjerg
Department of Energy Technology, Aalborg University, Pontoppidanstraede 101, Aalborg DK-9220, Denmark
[email protected], [email protected]
Abstract- The progressively growing of single-phase photovoltaic (PV) systems makes the Distribution System
Operators (DSO) to update or revise the existing grid codes in order to guarantee the availability, quality and reliability
of the electrical system. It is expected that the future PV systems connected to the low-voltage grid will be more active
with functionalities of low voltage ride-through (LVRT) and the grid support capability, which is not the case today. In
this paper, the operation principle is demonstrated for a single-phase grid-connected PV system in low voltage ride
through operation in order to map future challenges. The system is verified by simulations and experiments. Test results
show that the proposed power control method is effective and the single-phase PV inverters connected to low-voltage
networks are ready to provide grid support and ride-through voltage fault capability with satisfactory performance based
on the grid requirements for three-phase renewable energy systems.
1.
Introduction
More and more single-phase photovoltaic (PV) systems are
connected to the public grid mainly because of the matured
PV technology and the declined price of the PV module cell
[1]. As it is reported by PHOTON International, there was
27.7 GW of global PV generation systems installed in 2011,
nearly 21 GW in Europe, which makes accumulated installed
global PV capacity to be around 70 GW at the end of 2011. It
can be foreseen that the future grid-connected PV systems
will play a very important role in the regulation of the
conventional power systems.
However, behind the thriving penetration of single-phase
grid-connected PV systems, the phenomenon of large-scale
Distributed Generation (DG) systems connected to the public
grid also raises some concern on the availability, quality and
reliability of the grid. On this basis, many grid requirements
are published in recent years by the Transmission System
Operators, Distribution System Operators or international
standard committees (e.g. IEC and IEEE) in order to regulate
the interaction between DGs and the public grid [2]-[9]. In
spite of this fact, most of these grid requirements are focused
on three-phase wind power systems or DGs connected to
medium- or high-level grid. There are few grid codes and
papers describing the demands for PV systems connected to
low-level grid, like single-phase PV systems [6], [10]-[15].
Due to the fast growing installations of grid-connected PV
systems, it is expected that the future PV systems will be
more active and “smart” with the functionalities of low
voltage ride- through capability and grid support, which are
required for three-phase wind power systems. In the future,
the grid-connected PV system needs to fulfill the basic grid
requirements, like power quality demand, and also provides
some ancillary services like the conventional power plant
does. For instance, the PV inverters should inject some
reactive current when the grid presents a voltage sag fault. In
that case, the control strategies should be developed in order
to help the PV system ride-through during the grid faults.
For single-phase applications, the calculation of active and
reactive power is a big challenge, which leads to the
difficulty of direct instantaneous power control. Unlike threephase systems, it is difficult to employ directly a dq-rotating
synchronous reference frame in single-phase systems to
implement positive sequence control or constant reactive
power control [7], [8], [16]. Possible solutions for singlephase applications are based on the single-phase PQ theory,
instantaneous power control or the droop control concept
[13], [17]-[20]. Moreover, the grid fault detection and
synchronization techniques are also challenges for the singlephase system when operating in the grid fault mode.
In this paper, the overall control strategy for single-phase PV
systems in the grid faulty mode operation is demonstrated
based on the grid requirements defined for three-phase wind
power systems as it is expected that they will be the basic
requirements for single-phase PV systems. A transport delay
grid fault detection method is adopted in this study. A power
control method based on the single-phase PQ theory and the
proportional-resonant (PR) current control scheme is
proposed. Finally, the system is tested in simulation and
verified by experiments. The results show that the singlephase PV systems are ready for providing ancillary service in
the future and the grid detection method has a significant
impact on the performance of the single-phase PV systems
under grid faults.
2.
Grid Requirements
The grid requirements for DGs are updated and revised based
on the development and penetration level of DGs and issued
in the form of national grid code [2]-[6], such as E.ON grid
code and CEI grid code published by Comitato Elettrotecnico
Italiano. In these grid codes, the basic demands are imposed
like the power quality (the THD level of the injected current)
and the anti-islanding requirement. Considering the
penetration level of DGs connected to the grid, combined
requirements are expected to be added into the grid codes in
the future.
For example, in the German grid code, the DGs should
handle ride-through grid fault, known as Low Voltage RideThrough (LVRT) capability, and support the grid during the
voltage recovery. Similar requirements can be found in other
countries, like Denmark, Italy, Spain and USA in which the
DGs share a high percentage of power generation. The LVRT
capability is defined so that the DG should stay connected to
the grid within a short time and inject some reactive power to
support the grid when the grid presents a voltage fault.
Different LVRT curves with defined stay-connected time are
shown in Fig. 1.
V (p.u.)
1.00
0.90
0.70
Italy
∆Iq/IN
Dead band
Germany
Spain
Denmark
US-FERC
∆Iq/IN
≥ 2 p.u.
∆V/VN
k=
-50%
-10%
10%
∆Iq=Iq-Iq0
∆V=V-V0
-100%
Voltage Rise
Voltage Drop
Fig. 2. Voltage support requirement under grid faults for wind turbines [3].
3.
Single-Phase Grid-Connected Photovoltaic System in
the Grid Faulty Mode Operation
A. System Configuration
In consideration of the whole conversion efficiency, a singlestage PV system is connected to the grid through a
transformer, which is shown in Fig. 3. In some cases, a
voltage-boost stage can be used between the DC capacitor C
and the inverter, depending on the output voltage level of the
PV panels. The boost stage makes the system flexible to track
the Maximum Power Point (MPP) of the PV panel and also
makes it possible to handle the power variation across the DC
capacitor C at twice the grid fundamental frequency [9].
Inverter
PV ipv
L/2
S1
ig
S2
C
These grid requirements are set to ensure the safety of utility
maintenance personnel and also other devices connected the
public grid and to avoid the grid collapse due to voltage
faults. It is expected that these grid requirements will be
recommended to be used to regulate single-phase PV
systems, since the impact of large-scale single-phase PV
systems on the low-level public grid cannot be ignored. The
discussion in this paper is based on these requirements.
RL
L/2
Control System
ig
vg
N
vg
PWM
vpv
OSG based
Power Caculator
vgα vgβ
P Q
*
vPWM
*
vinv
Current
Controller
Grid
Rs
Cf
vinv
vpv
0.30
0.20
As it is shown in Fig. 1, the DGs should stay connected to the
grid when the voltage drops to 0 V in the German grid code
in 0.15 seconds. At the same time, the system should inject
some reactive current in order to support the grid recovery
according to Fig. 2.
20% ∆V/VN
Support the voltage
0.45
0 0.15
0.7
1.50
3.00 Time (s)
Fig. 1. Low voltage ride through (LVRT) requirements of distributed
generation systems in different countries [2], [5].
Limit the voltage
ig
ig*
Power
Controllers
Voltage Sag
Detection
P*
Q
*
Sag Signal
Power
Profiles
ipv
vpv
Fig. 3. Overall structure of a single-phase grid-connected PV system (OSG:
Orthogonal Signal Generator).
The control system shown in Fig. 3 consists of a voltage sag
detection unit, an Orthogonal Signal Generator (OSG) for
power calculation, the power profiles including MPPT
control in normal operation, active and reactive power
controllers for current reference generation, a grid current
controller and a PWM generation block.
As it can also be seen in Fig. 3, in order to implement grid
fault operation mode for this system, a voltage sag generator
is used by switching the series resistor Rs and the load
resistance RL. During the LVRT mode operation, the switch S1
is open in order to limit the short-circuit effect on the
upstream grid and the switch S2 is closed, while in normal
operation, S1 is closed and S2 is open.
An LC-filter ( LCf ) is used as the output filter in order to limit
the high-order harmonics coming from the inverter switching
behavior. Thus, neglecting all the filter losses, the system at
the AC side can be described by,
dig t dt
d 2 vg t v g t vinv t ,
Cf
L
dt 2
L
In this paper, the peak value method is used to detect the
voltage fault. The implementation of this method is easy, and
by means of the OSG system, it is possible and flexible to
calculate the average active and reactive power instantaneously. Since the T/4 Delay structure is used to build up the
OSG system as it is shown in Fig. 5, the system will
introduce a quarter period time delay of the input
fundamental period. The peak value of the input voltage can
be given by,
(1)
Vm
vg2 vcg2
Vm2 sin 2 Zt Vm2 cos2 Zt , (3)
in the time domain and
Ig s
1
1 ·
§
Vinv s ¨ C f s ¸Vg s ,
Ls
Ls ¹
©
(2)
in the Laplace domain, where ig is the injected grid current,
vinv is the inverter output voltage and vg is the grid voltage.
Hence, the equivalent model of the output filter can be given
as it is shown in Fig. 4.
vg
where vg’ is the orthogonal signal of the input voltage
generated by shifting a quarter period of the input signal.
LPF
vg
vg2
LPF
vg=Vmsin(ωt)
→
→
→
u2
Vm
2
vg’
T/4 Delay
LCf s2+1
vinv
u2
1
Ls
ig
Fig. 5. Voltage sag detection by monitoring the peak value based on T/4
Delay orthogonal system.
C. Power Calculation and Power Profiles
Fig. 4. Equivalent model of the output LC-filter in the Laplace domain.
B. Voltage Sag Detection
Grid condition information is very important for the control
system to perform special functionalities. Similarly, as a part
of the grid condition detection, the voltage sag detection is
the way to identify the voltage fault and it determines the
dynamic performance of the voltage sag compensator [21],
[24] and the behavior of the whole control system. It is easy
to understand that the system should switch from normal
operation mode to grid fault operation mode as soon as
possible, once the voltage sag is detected. Hence, it is
essential to have a precise and fast fault detection unit.
Recently, many voltage sag detection methods have been
proposed, such as Root Mean Square (RMS) method, peak
value method (OSG based sag detection techniques), the
missing voltage technique and wavelet transform method
[10], [21]-[25]. The RMS method computes the RMS value
of the input signal by using a running average window of one
cycle. Therefore, theoretically, this method will introduce one
cycle delay in order to give the correct value. The wavelettransform based voltage sag detection is becoming of high
interest [23], because of its fast detection speed. However, the
implementation of this method is unfortunately not easy in
real time.
In different operation modes, the power profiles are different.
Firstly, the average active power P and reactive power Q of
the system are computed using Discrete Fourier Transform
(DFT) structure, as it is shown in Fig. 6.
vg
DFT
ig
DFT
|u|
1/2
P
u
|u|
cos
u
sin
Q
Fig. 6. Power calculation based on Discrete Fourier Transform (DFT).
Under normal grid conditions, the system is operating in
Maximum Power Point Tracking (MPPT) mode in order to
deliver as much energy as possible to the grid, and the power
factor is normally near to one. According to the grid
requirements, in grid faulty mode operation, the single-phase
PV inverter should inject some reactive power into the grid to
support the grid voltage during recovery. The amount of
reactive power should be injected dependent on the voltage
sag depth and the inverter rating current. At the same time,
the PV panels should switch to non-MPPT operation mode in
order to avoid tripping the inverter overcurrent protection
[10], [26], [27]. The operation modes are described in Fig. 7.
ipv
vpv
MPPT
P*
Q*
Q*
the nominal grid voltage, IN, Iq0 are the nominal current and
the initial reactive current before a grid failure, and k =
(∆Iq/In)/(∆V/Vn) ≥ 2 p.u.. By substituting (6) into (4), the
required active power P* and reactive power Q* reference in
the grid faulty mode operation can be given as,
Normal Operation Mode
­ *
P
°
°
®
°Q*
°̄
Vm
P*
*
vpv
Q*
LVRT
Fig. 7. Power profiles for a single-phase grid-connected PV system in
different operation modes.
By employing Park transform (αβ → dq) to the grid voltage
and current in the OSG systems, the active power P and
reactive power Q delivered to the grid can also be calculated
and expressed as,
1
vgd igd
2
1
vgd igq
2
(4)
,
where the subscripts “gd” and “gq” denote the “d” and “q”
components of the grid voltage/current in a dq-rotating
synchronous reference frame.
1
Vmigd
2
1
Vmigq
2
1
Vm I m
2
| PPV , MPP
,
(5)
According to (7) and Fig. 7, the PV panels should “de-rate”
its output power when the grid presents a voltage fault, as it
can be illustrated in Fig. 8. The de-rated power level (PPV,MPP
→ P* or PPV) is dependent on the voltage sag depth and the
nominal current. If the voltage drop is small, either by
decreasing the PV voltage reference or increasing it can limit
the PV output power. However, it should be noted that the PV
voltage must be in the inverter input voltage range.
P
PPV,MPP
VN I m
2
Sag
Depth
P*
VIN
2
1
2
0
Q
In faulty grid operation mode, according to Fig. 2, the
required reactive current under voltage sags can be given as,
­ deadband,
0.9 p.u. d V 1.1 p.u.
°
° V V0
˜ I N I q 0 , 0.5 p.u. d V 0.9 p.u.
®k ˜
VN
°
° I N Iq0 ,
V 0.5 p.u.
¯
PPV,max
VNImax
2
0
in which Vm and Im are the amplitude of the grid voltage and
current in MPPT operation mode, respectively, PPV,MPP is the
tracked maximum output power of the PV panels.
Iq
(7)
IN .
Normally, the nominal current is limited by the inverter
maximum rating current, IN ≤ Imax, where Imax is the inverter
maximum rating current and the initial reactive current is
zero, Iq0 = 0 A.
As it is stated above, in normal MPPT operation mode, the
system is operating at unity power factor. Then, neglecting
the switching power losses, the active power P and reactive
power Q can be obtained,
­
P
°
°
®
°Q
°̄
I d2 I q2
,
where PPV is the output power of the PV panel in the grid
faulty mode operation.
Grid Fault Operation Mode
­
P
°
°
®
°Q
°̄
1
VI d | PPV
2
1
VI q
2
(6)
in which V, V0, and VN are the amplitude values of the grid
instantaneous voltage, initial voltage before grid faults and
Q*
Q
Fig. 8. PQ-diagram and PV power-voltage curve (black bold line) in different
operation modes: 1) MPPT mode and 2) grid fault mode.
D. Power Controllers and Current Reference Generation
Similar to the power calculation in the dq-rotating reference
frame, the active power P and reactive power Q for a singlephase application can be computed with the help of OSG
systems,
­
P
°
°
®
°Q
°̄
1
vgD igD vgE igE 2
1
vgE igD vgD igE 2
,
(8)
in which the subscripts “gα” and “gβ” denote the “α” and “β”
components of the grid voltage/current in a αβ-stationary
reference frame.
In this way, the currents in a αβ-stationary reference frame
can be expressed as,
ªigD º
«i »
¬ gE ¼
2
v vg2E
2
gD
ªvgD
«v
¬ gE
vg E º ª P º
vgD »¼ «¬Q »¼
(9)
.
controller (RC) [30] and PI control which needs a Park
transform (αβ → dq) [29], can be adopted in different
operation modes. In this case, the PR controller is used. For
the purpose of suppression of the injected current harmonics,
resonant harmonic compensation method is employed, which
is shown in Fig. 9.
Hence, the current closed-loop transfer function (ig(s)/ig*(s))
can be expressed as,
Since the active power and reactive power are DC quantities
in steady state, it is possible to use PI-controllers for power
regulation, and thus the current reference can be given by,
ªig*D º
«* »
«¬ig E »¼
vg2D
1
vg2E
ªvgD
«v
¬ gE
vg E º ª G p ( s ) P P º
«
» , (10)
vgD »¼ «G ( s) Q Q* »
¬ q
¼
ig s GPR HC s ˜ Gd s Ls GPR HC s ˜ Gd s i s
*
g
(12)
*
where “*” denotes the reference signal, Gp(s) and Gq(s) are
the transfer functions of the PI controllers for active power
and reactive power, respectively, and which can be given by,
1
­
G p ( s ) K pp K pi
,
°
°
s
®
° G ( s) K K 1 .
qp
qi
°̄ q
s
in which GPR+HC(s) is the transfer function of PR controller
with harmonics compensation, and Gd (s) is the processing
and PWM delay [28]. GPR+HC(s) and Gd (s) have the following
expressions:
GPR HC s Gd s The existing current control methods, such as Proportional
Resonant (PR) [28], [29], Deadbeat control (DB), Repetitive
ig
¦
3,5,7,...
kih s
s hZ0 2
2
,
1
,
1 1.5Ts s
where kp is the proportional gain, ki and kih are the resonant
and harmonic compensator gains, h is the harmonic order, ω0
is the fundamental frequency and Ts is the sampling period.
PR Controller
k p+
ki s
s Z02 h
2
(11)
E. Current Controller with Harmonic Compensation
ig*
kp Delay
v*inv
kis
s2+ω02
vinv
1
1+1.5Tss
Harmonic Compensators
1
Ls
ig
LCf s2+1
kihs
2
s +(hω0)2
vg
PR+HC
Fig. 9. Current control loop with PR controller and harmonic compensation to eliminate harmonic voltage distortion.
vgα
P
P*
Gp(s)
Q*
2
vgα+vgβ
LCf s2+1
ig*
Gq(s)
Q
vg
2
GPR+HC(s)
v*inv
vinv
1
1+1.5Tss
1
Ls
ig
ig
vgβ
Fig. 10. Control diagram of a single-phase grid-connected system with PR controller and harmonic compensators based on single-phase PQ theory.
4.
Simulation and Experimental Results
Referring to Fig. 3 and Fig. 10, the whole system is simulated
in MATLAB in order to verify the performance of the
proposed power control method. In this system, the PV panel
is modeled by means of a 3-D lookup table [33]. The nominal
maximum power PPV,MPP is 1030 W, the voltage VPV,MPP and
current IPV,MPP at the maximum power point are 400 V and
2.56 A, respectively. The Incremental Conductance (INC)
MPPT method is adopted to capture the maximum output
power of the PV system. This INC method is modified
according to Fig. 7 and Fig. 8 in order to limit the output
power when the grid voltage drops, presenting a grid fault.
The other simulation parameters are listed in TABLE I. The
PI controller parameters for this simulation are kpp= 6.2, kpi=
1.5, kqp= 1, and kqi= 50. Simulation results are provided in
Fig. 12 and Fig. 13.
L = 3.6 mH, Cf = 2.35 μF
Transformer Leakage Inductance
and Resistance
Lg = 4 mH, Rg= 0.02 Ω
Sampling and Switching Frequency
fs = fsw = 10 kHz
As it is shown in Fig. 12 and Fig. 13, the single-stage singlephase PV system is subjected to a grid fault (about 0.35 p.u.)
at t = 0.7 s. This voltage sag lasts for about 320 ms. Since the
detection unit needs a few milliseconds (∆t) to give the
correct operation condition of the grid, instead of immediate
response, the MPPT and the control units continue to operate
as in a normal condition and thus the grid current rises in this
time interval. It happens similarly after the fault is cleared.
Once the grid fault is detected, the MPPT unit is disabled and
the control system is switched to grid fault operation mode as
it is shown in Fig. 7. Soon after, the system starts to inject
reactive current as required and limit the active power output
to prevent the inverter from over-current protection. After the
fault is cleared (voltage rises to 0.9 p.u.), the system goes
back to its normal operation, and again, it is trying to track
the maximum output power of the PV panels. However, as it
is shown in Fig. 12 and Fig. 13, it may take some time
because of the MPPT perturbing process.
Recovery
ig
vg
(a)
P
Q
Grid Current (A)
Voltage Sag
Reactive Power (Var)
It is also worth to point out that the voltage variation of the
DC capacitor (DC-link voltage) at the twice of the grid
fundamental frequency will introduce even harmonics in the
injected current. Moreover, in faulty grid operation mode, this
distortion is much more severe. In this case, the harmonic
compensation method by cascading several resonant
controllers will cause heavy computation burden and become
less practical, when the higher order harmonics need to be
compensated [30].
ω0 = 2π×50 rad/s
LC Filter
(b)
Time (s)
Grid Current (A)
Frequency (Hz)
Fig. 11. Open loop (blue) and closed loop (black) Bode diagrams of the
current controller with different sets of kih: kp = 22, kih = 500 (solid line) and
kih = 5000 (dashed line), where h = 1, 3, 5, 7.
Grid Frequency
Grid Voltage (V)
5ω0
7ω0
VN = 325 V
Grid Voltage Amplitude
Active Power (W)
3ω0
TABLE I
SIMULATION AND E XPERIMENTAL P ARAMETERS
Grid Voltage (V)
ω0
Phase (deg)
Magnitude (dB)
Hereafter, according to the above illustration, the whole
control diagram can be structured, as it is shown in Fig. 10. It
can be seen from Fig. 9 and Fig. 10 that the harmonics in the
grid voltage vg will propagate to the grid current reference ig*.
However, the cascaded harmonic compensators will suppress
the harmonics if the gains around the resonance frequencies
are high enough. The Bode diagram of the PR controller with
selective harmonics compensation is shown in Fig. 11, which
can be used to tune the parameters, kp, ki and kih. It is shown
in Fig. 11 that the selection of a large kih leads to a wide
frequency band around the resonance point [8].
ig
vg
(c)
Time (s)
Fig. 12. Simulation results for a single-phase PV system under grid fault:
(a) grid voltage and current; (b) active and reactive power; (c) grid voltage
and current during LVRT.
PV Power (W)
Voltage Sag
Recovery
LC Filter
Cf
Danfoss
Inverter
dSPACE
Control Desk
Delta DC
3Ø
Transformer
S1,S2
∆t
Time (s)
(a)
PV Power (W)
L
RS
MPP
RL
MPPT Operation
Grid Fault
Operation
PV Voltage (V)
(b)
Fig. 13. Simulation results for a single-phase PV system under grid fault:
(a) PV panel output power; (b) PV panel output power vs its voltage.
In order to validate the effectiveness of the proposed control
method, the system is also tested experimentally. Instead of
some real PV panels, two DC sources are used as the input
power. The whole system consists mainly of
x Two Delta Elektronika SM 300-5 DC power supply,
the nominal DC voltage, VDC = 400 V,
x Two DC capacitors connected in parallel, the
equivalent capacitance, C = 1100 μF,
x A Danfoss VLT FC302 3-phase inverter which is
configured as a single-phase inverter,
x A sag generator as shown in Fig. 3, Rs = 19.2 Ω and RL
= 20 Ω,
x A 5 kVA 3-phase transformer with leakage inductance
Lg= 2 mH and resistance Rg= 0.01 Ω per phase and,
x A DS 1103 dSPACE control system.
The PI controller parameters for active power regulation are
kpp= 1.2 and kpi= 50, while the parameters for reactive power
control are kqp= 1, and kqi= 50. The other parameters of the
single-phase system are shown in TABLE I. A voltage drop is
generated by switching the manual switches S1 and S2, which
are shown in Fig. 14. The experimental results are given in
Fig. 15.
As it is shown in the experimental results, when the grid is
subjected to a voltage sag (0.45 p.u.), the detection and
control units of the single-phase system cannot react to this
sudden change immediately, and thus the grid current is going
to enter into a zone where the current reference is not
appropriate until the detection unit output the sag signal.
During the LVRT operation mode, the system is injecting
some reactive power into the power grid and at the same time
the active power is limited in consideration of the current
Fig. 14. Experimental setup of a single-phase grid-connected system.
limitation of the PV inverter, which is shown in Fig. 15 (b).
When the voltage sag is cleared (the voltage amplitude goes
to 90% of the nominal value), the system returns to its normal
operation mode and is injecting current at unity power factor.
It is also shown in Fig. 15 that both the start of the voltage
sag and the end of that present a transient time delay (∆t1 and
∆t2) which is approximately 5 ms (T/4). Firstly, it is because
of the fault detection time delay (T/4 Delay sag detection
method) as illustrated in previous paragraph. The power
profile might be another reason since it is a step change when
the voltage goes back to 90% of the nominal value. The
response of the current controller may deteriorate the
dynamics as well. Therefore, fast and accurate grid detection
and reasonable power profile are necessary for a single-phase
system in the grid fault mode operation.
However, the simulation and experimental results demonstrate the flexibility of a single-phase system to provide grid
support functionality. The power control method in the test is
effective to do so and it can do it fast.
5.
Conclusion
Based on the existing grid requirements, this paper discussed
the potential of a single-stage single-phase system operating
in grid fault condition. The power control method proposed in
this paper is effective when the system is switched to grid
fault operation mode. It can be concluded that the future
single-phase grid-connected PV systems are ready to be more
active and more “smart” in the regulation of power grid. Like
the conventional generation systems, the single-phase PV
systems can also offer some ancillary service in the presence
of an abnormal grid condition. However, the performance is
dependent of the grid detection and control methods.
Acknowledgement
The authors would like to thank China Scholarship Council
(CSC) for supporting this PhD project in the Department of
Energy Technology at Aalborg University, Denmark.
Voltage Sag
P
Q
ig
vg
(a)
(b)
Voltage Sag
ig
ig
vg
∆t2
vg
∆t1
(c)
(d)
Fig. 15. Experimental results of a single-phase system under grid fault based on the single-phase PQ theory and T/4 Delay sag detection method:
(a) grid voltage [vg: 100 V/div] and grid current [ig: 5 A/div]; (b) active power [P: 500 W/div] and reactive power [Q: 500 Var/div]; (c) dynamic performance of
grid voltage and current at the start of sag and (d) dynamic performance of grid voltage and current at the end of sag.
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